A bird perched on a swing the sits 8 cm below a bar has a mass of 52 g, and the base of the swing has a mass of 153 g. The swing and bird are originally at rest, and then the bird takes of horizontally at 2 m/s. How high will the base of the swing rise above its original level (disregard friction)?

Use conservation of momentum:

massbird(vbird)=massswing*velswing

then, having the velocit of swing, determine its KEnergy. That kE will equal gravitational PE, or mgh.

height= 1.2898x10^-3

To solve this problem, we will first use the principle of conservation of momentum to determine the initial velocity of the swing when the bird takes off horizontally.

According to the conservation of momentum principle, the momentum before and after an interaction remains constant, as long as no external forces act on the system. In this case, the system consists of the bird and the swing.

Using the principle of conservation of momentum, we can write the equation as:

mass_bird * velocity_bird = mass_swing * velocity_swing

where mass_bird is the mass of the bird, velocity_bird is the horizontal velocity of the bird, mass_swing is the mass of the swing including the base, and velocity_swing is the horizontal velocity of the swing.

Given the information provided in the problem:

mass_bird = 52 g = 0.052 kg
velocity_bird = 2 m/s
mass_swing = 153 g = 0.153 kg

Plugging these values into the equation:

0.052 kg * 2 m/s = 0.153 kg * velocity_swing

Simplifying the equation:

0.104 kg m/s = 0.153 kg * velocity_swing

Dividing both sides of the equation by 0.153 kg:

velocity_swing = 0.104 kg m/s / 0.153 kg
velocity_swing ≈ 0.68 m/s

Now that we have the velocity of the swing, we can determine how high the base of the swing will rise above its original level by treating the change in kinetic energy of the swing as the gravitational potential energy.

The kinetic energy of an object is given by the equation:

KE = 1/2 * mass * velocity^2

So, the kinetic energy of the swing is:

KE_swing = 1/2 * mass_swing * velocity_swing^2

Plugging in the values:

KE_swing = 1/2 * 0.153 kg * (0.68 m/s)^2
KE_swing ≈ 0.043 J

The potential energy of the swing at its highest point is equal to the change in kinetic energy, which is given by the equation:

PE = mass * gravitational acceleration * height

Solving for height:

height = PE / (mass_swing * gravitational acceleration)

Given that the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the height:

height = 0.043 J / (0.153 kg * 9.8 m/s^2)
height ≈ 0.028 m

Therefore, the base of the swing will rise approximately 0.028 meters (or 2.8 cm) above its original level.